Complex dynamics of 1.3.5-trimethylbenzene-2.4.6-D3 studied by proton spin–lattice NMR relaxation and second moment of NMR line

Abstract

Molecular dynamics of a solid 1.3.5-trimethylbenzene-2.4.6-D3 in phase I is studied on the basis of the proton T1 (24.7MHz and 15MHz) relaxation time measurements and the proton second moment of NMR line, M2. The measurements of the T1 were performed for temperatures from 20 to 167K, while those of the second moment M2 from 23 to 220K. The phase I was accurately prepared. The obtained second moment, M2 values were correlated with those based on T1 relaxation time measurements. The proton spin pairs of the methyl groups perform a complex motion being a resultant of two components characterized by the correlation times τ3T and τ3H, referring to the tunneling and over the barrier jumps in a triple potential. Forτ3Hthe Arrhenius temperature dependence was assumed, while forτ3T – the Schrödinger one. The jumps over the barrier causes a minimum in T1 (24.7MHz) at temperature about 35K. The high temperatures slope of this minimum permits evaluation of the activation energy as EH=2.0kJ/mol. The relaxation time T1 is temperature independent in the lowest temperature regime. This indicates that tunnelling correlation time assumes a constant value of about 1.3·10-10s according to the Schrödinger equation (τ3T≈τ03TeBEH at lowest temperatures). The tunneling jumps of methyl protons reduce M2 from the rigid lattice value 22.6G2 to the value 5.7G2 at zero Kelvin temperature. The second reduction to the value 1.41G2 at 4.5–7K is due to C3 jumps over the barrier. According to the Schrödinger equation the tunnelling jumps ceases above Ttun temperature where the thermal energy is equal to the activation energy. The Ttun equals 43.8K (from T1 data fit, EH=2.0kJ/mol) or 35K (from M2 data fit, EH=1.47kJ/mol). The second moment assumes again the value 5.7G2 above Ttun temperature.The tunneling splitting, ωT, was estimated equal 2.47GHz as best fit parameter from the T1 fit. The symmetrical T1 minimum indicates the same value of ωT for the all methyl groups. This frequency is in good agreement with the value of ωT (ℏωT=10.2μeV, tunnel splitting energy) obtained from the neutron powder scattering method. This high tunneling splitting is responsible for the long and Larmor frequency independent of T1 relaxation time. The presented results are compared to those of Köksal et al.